Also my cpu has a little bit thermal paste
....
It's very hard to tell much of anything about either the socket or CPU's pin condition from those pictures as they're quite fuzzy.
Check the CPU pins by looking at the CPU sideways and down each row and column. You're looking for a pin that's not in alignment with the others. Pins that are slightly out of alignment can be straightened back by simply sliding a credit card between each row and along each column.
Pins that are grossly misaligned need to be pushed back to vertical using something like a needle. One tool that's especially good is a Pentel pencil with the lead removed: slide the empty 'barrel' over the bent pin and straighten it.
Do not fret thermal paste so long as it's not excessive... which it doesn't appear to be from those pictures. It's harmless and you're more likely to cause real damage by attempting to remove it.
The socket is more difficult to check. I do it by using a bright light and scan along each row looking at the gleaming reflection that comes off each contact in the socket. I'm looking for anything that may be different. When I'm satisfied I place the CPU on the socket (mind orientation). It should drop into place with only gentle jiggling side to side. If it's not, remove it and check again for bent pins. If it simply will not drop into place you may have a bent or damaged socket contact.